Latest TCS Aptitude Question SOLUTION: What will be the remainder when (222)^222 is divided by 7?

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What will be the remainder when
(222)^222 is divided by 7?

Asked In TCS max (10 years ago)

Solved pappu gupta Read Solution (10)

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pappu gupta  (10 years ago)

(7*31+5)^222 /7

5^222 /7

(5^2)^111 /7
(7*3+4)^111/7
(4^111)/7
(2^3)^37/7
(7+1)^37/7
so, 1/7
i.e remainder=1 ansr

Is this solution Helpfull? Yes (47) | No (5)  

pappu gupta  (10 years ago)

(7*31+5)^222 /7

5^222 /7

(5^2)^111 /7
(7*3+4)^111/7
(4^111)/7
(2^3)^74/7
(7+1)^74/7
so, 1/7
i.e remainder=1 ansr sry previous 1 has a little mistake bt this 1 is right

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Arindam Dhara  (10 years ago)

rem of (222/7)= 5
so now rem of (5^222)/7

now checking cyclicity of rem in 5's power when dvided by 7
rem(5/7)=5
rem(25/7)=4
rem(125/7)=6
rem(625/7)=2
rem(3125/7)=3
rem(15625/7)=1

it repeats after 6 iteration.
so rem(222/6)=0

so rem of (222)^222 is divided by 7 is 1

Is this solution Helpfull? Yes (13) | No (3)  

shubhankar barman  (10 years ago)

(2+2+2)^(2+2+2)
6^6
=46656
now 46656/7=1 reminder
ans is reminder=1

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pratik jitendra malviya  (10 years ago)

ans.1 222^222 means unit digits are 2,4,8,6 this digit repeat again &again hence
222/4=55 & means the 3rd digit repetition 8/7=1

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Guru Pranav  (10 years ago)

222^222/7= 5^222/7=125^74=(-1)^74/7=1 Ans.

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Shrikant  (10 years ago)

(17*13+1)^222
(1)^222
anything to the power 1 is 1
so rem is 1...

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amit kumar burnwal  (10 years ago)

remainder w'll be 1

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tarun kosta  (10 years ago)

Ans is 1 ,its very easy, simply apply reminder theorem :)

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prem kumar shaw  (10 years ago)

firtst divide base by 7 then find remainder then if diviser is prime then substract by 1 and divide power by new diviser
222/7=5 rem and here 7 is prime so new diviser =7-1=6 and 222/6=0 rem
now 5^0/7=1rem

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